Sigma-delta (ΣΔ) (or delta-sigma (ΔΣ)) modulation is a known method for encoding analogue signals into digital signals or higher-resolution digital signals into lower-resolution digital signals. The conversion is done using negative feedback, where the difference between the two signals is measured and used to improve the conversion. This conversion technique may be used in electronic components such as Analog-to-digital converters (ADCs), digital-to-analog converters (DACs), frequency synthesizers, switched-mode power supplies and motor controllers.
A sigma-delta modulator is a feedback system consisting of a loop filter (with transfer function generally denoted as H(s)), an ADC (or quantizer), and a DAC in the feedback path. Such a basic conventional configuration is shown in FIG. 1.
A sigma-delta modulator is oversampled. In combination with the feedback path and the loopfilter, the quantization error is approximately shaped according to the inverse of the loopfilter characteristic in the frequency region where the loopfilter gain is high. The quantization error of the quantizer ADC is in this way suppressed in a signal band of interest.
For frequencies where the loopfilter gain decreases, the quantization noise increases. However, by means of a digital decimation filter at the output of the sigma-delta modulator, the out-of-band increasing quantization noise is filtered away and very high resolutions can be achieved in relatively small bandwidths.
The loopfilter H(s) of the sigma-delta modulator of FIG. 1 can be implemented in several ways, and the so-called distributed feed-forward topology and the feedback topology are the most common implementations.
FIG. 2 shows a typical 4th-order architecture with distributed feed-forward paths. The circuit 10 comprises four integrator stages Int1 to Int4. There is a feed forward from the output of each integrator to the output of the loop filter. The loop filter output is fed to an ADC 20. The circuit has a negative feedback path to the input of the first integrator stage. The digital output from ADC 20 is converted to an analogue signal by a first DAC 22, which provides the analogue signal to the input of the first integrator Int1. Typically, another feedback path with a second DAC 24 provides an analogue signal to the output of the loop filter. This optional second feedback path compensates for excess delays in the ADC 20 and feedback DAC 22.
FIG. 3 shows an example of a possible signal transfer function (STF) for the 4th-order sigma-delta modulator of FIG. 2. It is seen that the STF is flat for a small frequency band and then increases for higher frequencies. The out-of-band STF gain can reach 20 dB or higher values, depending on the coefficients of the loop filter. This is inherent to the feed-forward architecture.
Thus, it will be appreciated that a distributed feed-forward architecture, such as that shown in FIG. 2, exhibits the drawback that the STF of the modulator exhibits out-of-band peaking very close to the signal bandwidth.